mlsanityData to 7 Oct 2026

GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation

arXiv 2203.02923 ↗First posted 6 Mar 2022cs.LG q-bio.QMcited by 511

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Predicting molecular conformations from molecular graphs is a fundamental problem in cheminformatics and drug discovery. Recently, significant progress has been achieved with machine learning approaches, especially with deep generative models. Inspired by the diffusion process in classical non-equilibrium thermodynamics where heated particles will diffuse from original states to a noise distribution, in this paper, we propose a novel generative model named GeoDiff for molecular conformation prediction. GeoDiff treats each atom as a particle and learns to directly reverse the diffusion process (i.e., transforming from a noise distribution to stable conformations) as a Markov chain. Modeling such a generation process is however very challenging as the likelihood of conformations should be roto-translational invariant. We theoretically show that Markov chains evolving with equivariant Markov kernels can induce an invariant distribution by design, and further propose building blocks for the Markov kernels to preserve the desirable equivariance property. The whole framework can be efficiently trained in an end-to-end fashion by optimizing a weighted variational lower bound to the (conditional) likelihood. Experiments on multiple benchmarks show that GeoDiff is superior or comparable to existing state-of-the-art approaches, especially on large molecules.

Key facts. Cited by 511 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 36 of its 57 references that are in the map. First posted on arXiv 6 Mar 2022.

Builds on

36 of 57 references.

References · 36

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Denoising Diffusion Implicit Modelscited by 9,655
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  5. 2013Auto-Encoding Variational Bayescited by 3,980
  6. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  7. 2016A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networkscited by 2,362
  8. 2016Density estimation using Real NVPcited by 2,029
  9. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  10. 2021E(n) Equivariant Graph Neural Networkscited by 951
  11. 2015Convolutional Networks on Graphs for Learning Molecular Fingerprintscited by 751
  12. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
24 more
  1. 2021Diffusion Probabilistic Models for 3D Point Cloud Generationcited by 734
  2. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  3. 2018Junction Tree Variational Autoencoder for Molecular Graph Generationcited by 647
  4. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  5. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 569
  6. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  7. 2020Implicit Functions in Feature Space for 3D Shape Reconstruction and Completioncited by 343
  8. 2020Learning from Protein Structure with Geometric Vector Perceptronscited by 308
  9. 2020GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generationcited by 301
  10. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 248
  11. 2020GEOM: Energy-annotated molecular conformations for property prediction and molecular generationcited by 238
  12. 2017Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanicscited by 213
  13. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 162
  14. 2021GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensemblescited by 106
  15. 2021Inverse design of 3d molecular structures with conditional generative neural networkscited by 93
  16. 2019Molecular geometry prediction using a deep generative graph neural networkcited by 91
  17. 2021Learning Neural Generative Dynamics for Molecular Conformation Generationcited by 87
  18. 2019A Generative Model for Molecular Distance Geometrycited by 73
  19. 2021An End-to-End Framework for Molecular Conformation Generation via Bilevel Programmingcited by 59
  20. 2020Symmetry-Aware Actor-Critic for 3D Molecular Designcited by 55
  21. 2021Rotation Invariant Graph Neural Networks using Spin Convolutionscited by 52
  22. 2020Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Propertiescited by 51
  23. 2022Direct Molecular Conformation Generationcited by 30
  24. 2020TorsionNet: A Reinforcement Learning Approach to Sequential Conformer Searchcited by 15

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 51; 2023: 143; 2024: 129; 2025: 115; 2026: 73.

511 papers.

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  1. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  2. 2023Training Diffusion Models with Reinforcement Learningcited by 939
  3. 2022DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Modelscited by 924
  4. 2022eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoiserscited by 921
  5. 2022On Distillation of Guided Diffusion Modelscited by 721
  6. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  7. 2022Executing your Commands via Motion Diffusion in Latent Spacecited by 567
  8. 2022DiGress: Discrete Denoising diffusion for graph generationcited by 503
  9. 2023InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generationcited by 387
  10. 2022DiffusionDet: Diffusion Model for Object Detectioncited by 354
  11. 2024Retrieval-Augmented Generation for AI-Generated Content: A Surveycited by 352
  12. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
38 more
  1. 2023Q-Diffusion: Quantizing Diffusion Modelscited by 266
  2. 2022Torsional Diffusion for Molecular Conformer Generationcited by 262
  3. 2023Efficient Diffusion Training via Min-SNR Weighting Strategycited by 242
  4. 2022A Survey on Generative Diffusion Modelcited by 238
  5. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localizationcited by 230
  6. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 229
  7. 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 216
  8. 2023SE(3) diffusion model with application to protein backbone generationcited by 214
  9. 2022Structure-based Drug Design with Equivariant Diffusion Modelscited by 213
  10. 2022DiffRF: Rendering-Guided 3D Radiance Field Diffusioncited by 204
  11. 2023Geometric Latent Diffusion Models for 3D Molecule Generationcited by 185
  12. 20233D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Predictioncited by 176
  13. 2022Fast Sampling of Diffusion Models via Operator Learningcited by 173
  14. 2023UFOGen: You Forward Once Large Scale Text-to-Image Generation via Diffusion GANscited by 165
  15. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  16. 2023Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learningcited by 145
  17. 2024Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Datacited by 143
  18. 2023Crystal Structure Prediction by Joint Equivariant Diffusioncited by 142
  19. 2024Beyond Autoregression: Discrete Diffusion for Complex Reasoning and Planningcited by 135
  20. 2023Equivariant flow matchingcited by 131
  21. 2023DiffusionSat: A Generative Foundation Model for Satellite Imagerycited by 130
  22. 2022GENIE: Higher-Order Denoising Diffusion Solverscited by 127
  23. 2022Pre-training via Denoising for Molecular Property Predictioncited by 124
  24. 2024Unlocking Guidance for Discrete State-Space Diffusion and Flow Modelscited by 124
  25. 2023On Memorization in Diffusion Modelscited by 122
  26. 2022Equivariant 3D-Conditional Diffusion Models for Molecular Linker Designcited by 121
  27. 2023Machine Learning for Synthetic Data Generation: A Reviewcited by 118
  28. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 113
  29. 2023Parallel Sampling of Diffusion Modelscited by 112
  30. 2023Affordance Diffusion: Synthesizing Hand-Object Interactionscited by 110
  31. 2022Diffusion-based Molecule Generation with Informative Prior Bridgescited by 104
  32. 2023DiffiT: Diffusion Vision Transformers for Image Generationcited by 104
  33. 2024TFG: Unified Training-Free Guidance for Diffusion Modelscited by 103
  34. 2022How to Backdoor Diffusion Models?cited by 102
  35. 2022Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Modelscited by 97
  36. 2023MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generationcited by 96
  37. 2022Exploring Chemical Space with Score-based Out-of-distribution Generationcited by 95
  38. 2024Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Reviewcited by 92

50 most cited of 511 All 511 (JSON)

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  1. 2026Geometric Flow Matching for Molecular Conformation Generation via Manifold Decomposition
  2. 2024Geometric-Facilitated Denoising Diffusion Model for 3D Molecule Generation
  3. 2024Physics-informed generative model for drug-like molecule conformers
  4. 2024Accelerating the Generation of Molecular Conformations with Progressive Distillation of Equivariant Latent Diffusion Models
  5. 2025Unlocking hidden biomolecular conformational landscapes in diffusion models at inference time
  6. 2025DiffMS: Diffusion Generation of Molecules Conditioned on Mass Spectra
  7. 2025EquiBoost: An Equivariant Boosting Approach to Molecular Conformation Generation
  8. 2025Generative Modeling of Full-Atom Protein Conformations using Latent Diffusion on Graph Embeddings